A precision apparatus for high harmonic spectroscopy in bulk solids

TL;DR

The paper addresses the challenge of performing quantitative high harmonic spectroscopy in bulk solids by requiring stable driving fields, precise crystal orientation, and broadband detection. It introduces an integrated apparatus that combines dispersion-neutral intensity control, a vacuum HHG module, imaging/spatial filtering, dual UV/VUV–EUV spectrometers, and external attosecond streaking for absolute field calibration. The authors validate the system with representative measurements on fused silica and MgO, demonstrating stable, field- and angle-resolved HHG with high precision. This platform offers a robust, adaptable tool for mapping electronic structure, reconstructing valence-electron potentials, and tracking strong-field dynamics with sub-cycle temporal resolution across diverse materials and laser sources.

Abstract

High harmonic generation (HHG) in solids has emerged as a powerful spectroscopic method for resolving ultrafast electron dynamics and band structure properties across a wide range of materials. However, quantitative HHG studies require instrumentation capable of delivering stable driving fields, precise crystal alignment, and broadband detection spanning the UV to the extreme ultraviolet (EUV). Here we present an integrated apparatus engineered specifically for high-accuracy, field-strength and orientation-dependent HHG measurements in bulk solids. The system incorporates dispersion-neutral intensity-control for few-cycle pulses, a vacuum HHG module with sub-micrometer and sub-degree sample positioning, and an imaging assembly that stabilizes the focal spot position and enables spatial filtering of the emitted harmonics. A synchronized dual-spectrometer scheme provides simultaneous UV/VUV and EUV radiation detection, while absolute electric field calibration is achieved through gas-phase attosecond streaking. Together, these capabilities establish a versatile and quantitatively reliable platform for solid-state HHG spectroscopy. The methodology is broadly adaptable to various laser sources and material classes, and supports future efforts aimed at reconstructing valence-electron potentials, tracking strong-field dynamics, and mapping electronic structure with sub-cycle temporal resolution.

Figures (9)

• Figure 1: Schematic of the high harmonic spectroscopy apparatus.
• Figure 2: Intensity control module and TG-FROG. (a) Schematic of the visible (yellow) and NIR (red) pulse compressor with the variable ND filter. Pulses from LFS are negatively chirped by chirped mirrors (CM) and dispersed by a pair of wedges in each individual path. Metal-coated mirrors are marked as MM. (b) Schematic of the TG-FROG setup for temporal characterization of the pulse (see also reference Sweetser1997).
• Figure 3: Temporal characterization of the pulses used in high harmonic generation experiments. (a), (b) Measured TG-FROG spectrograms of the driving pulses centered at 2 eV and 1.5 eV respectively. (c), (d) Retrieved temporal intensity profile (blue) and phase (red). The evaluated pulse durations at the FWHM are $\tau_{\mathrm{VIS}}$$\simeq$ 6.9 fs and $\tau_{\mathrm{NIR}}$$\simeq$ 8.6 fs respectively.
• Figure 4: (a) Overview of the f-to-2f imaging system used for aligning the rotation axis of the crystal sample along the laser propagation axis (orange solid arrow). (b) Multi-axis goniometer with the sample holder. The green dashed arrows denote the axes of rotation of each rotation stage (c) Photograph of the sample holder with three mounted samples and a crosshair. (d), (e) Photograph of the crosshair and sample respectively. (f) The crosshair imaged at the focal plane.
• Figure 5: EUV spectrometer design. (a), (b) Design of the EUV spectrometer for measuring high harmonics emission driven by visible and NIR driving pulses respectively. The optimal arrangement (imaging of the source and maximal bandwidth) is attained when the MCP detector is placed at a distance of 17 cm from the center of the grating. Harmonic orders (first order diffraction) are denoted by numbers such as 3$^{\mathrm{rd}}$, 5$^{\mathrm{th}}$, 7$^{\mathrm{th}}$ and so on.